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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/adjoints/adjoints_ex2" target="_blank">Open adjoints_ex2 in new tab.</a>
<a name="output"></a> 
<br><br><br> <h1> The console output of the program: </h1> 
<pre>
***************************************************************
* Running Example adjoints_ex2:
*   example-opt  
***************************************************************
 
Started /Users/petejw/projects/libmesh_git/build/examples/adjoints/adjoints_ex2/.libs/example-opt
Reading in and building the mesh
Building system
Initializing systems
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=225
    n_local_nodes()=225
  n_elem()=63
    n_local_elem()=63
    n_active_elem()=48
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=1
   System #0, "LaplaceSystem"
    Type "Implicit"
    Variables="T" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" 
    Approximation Orders="SECOND", "THIRD" 
    n_dofs()=225
    n_local_dofs()=225
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 14.2267
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 25
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

  Nonlinear solver converged, step 0, residual reduction 8.17282e-14 < 1e-09
*** Warning, This code is deprecated, and likely to be removed in future library versions! ./include/libmesh/parameter_pointer.h, line 66, compiled Apr 12 2016 at 11:10:14 ***
Adaptive step 0, we have 48 active elements and 225 active dofs.
Sensitivity of QoI one to Parameter one is 0.00543563
Sensitivity of QoI one to Parameter two is 0.0108713
The relative error in sensitivity QoI_0_0 is 0.00027992857829232536
The relative error in sensitivity QoI_0_1 is 0.00027992861138438044

Refining Uniformly

Refined mesh to 192 active elements and 833 active dofs.
  Nonlinear solver converged, step 0, residual reduction 3.6773152841465795e-12 < 1.0000000000000001e-09
Adaptive step 1, we have 192 active elements and 833 active dofs.
Sensitivity of QoI one to Parameter one is 0.0054364698951489708
Sensitivity of QoI one to Parameter two is 0.010872939787948713
The relative error in sensitivity QoI_0_0 is 0.00012463766722315385
The relative error in sensitivity QoI_0_1 is 0.00012463788325784412

Refining Uniformly

Refined mesh to 768 active elements and 3201 active dofs.
  Nonlinear solver converged, step 0, residual reduction 2.6268364096092453e-11 < 1.0000000000000001e-09
Adaptive step 2, we have 768 active elements and 3201 active dofs.
Sensitivity of QoI one to Parameter one is 0.0054368750517143054
Sensitivity of QoI one to Parameter two is 0.010873750103093405
The relative error in sensitivity QoI_0_0 is 5.0121285199775726e-05
The relative error in sensitivity QoI_0_1 is 5.0121316024978454e-05

Refining Uniformly

Refined mesh to 3072 active elements and 12545 active dofs.
  Nonlinear solver converged, step 0, residual reduction 2.1868911779851296e-10 < 1.0000000000000001e-09
Adaptive step 3, we have 3072 active elements and 12545 active dofs.
Sensitivity of QoI one to Parameter one is 0.0054370390298797552
Sensitivity of QoI one to Parameter two is 0.010874078058782268
The error in sensitivity QoI_0_0 is 1.9962426463146358e-05
The error in sensitivity QoI_0_1 is 1.9962516330039864e-05


 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 10:21:24 2016                                                                          |
| OS:             Darwin                                                                                            |
| HostName:       peterson-laptop.local                                                                             |
| OS Release:     15.0.0                                                                                            |
| OS Version:     Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64  |
| Machine:        x86_64                                                                                            |
| Username:       petejw                                                                                            |
| Configuration:  ../configure  'INSTALL=/usr/bin/install -C'                                                       |
|  '--with-methods=opt dbg'                                                                                         |
|  '--prefix=/Users/petejw/projects/libmesh_git/installed'                                                          |
|  '--enable-perflog'                                                                                               |
|  '--enable-tracefiles'                                                                                            |
|  '--disable-blocked-storage'                                                                                      |
|  '--enable-default-comm-world'                                                                                    |
|  '--enable-tecio'                                                                                                 |
|  '--enable-unique-ptr'                                                                                            |
|  '--enable-ifem'                                                                                                  |
|  'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu'                                                 |
|  'SLEPC_DIR=/opt/petejw/slepc/3.6.1'                                                                              |
|  'CPPFLAGS= '                                                                                                     |
|  'LIBS= '                                                                                                         |
|  'CPPFLAGS=  '                                                                                                    |
|  'LIBS=  '                                                                                                        |
|  '--disable-netcdf-4'                                                                                             |
|  '--disable-testsets'                                                                                             |
|  'CXX=mpicxx'                                                                                                     |
|  'CC=mpicc'                                                                                                       |
|  'F77=mpif77'                                                                                                     |
|  'FC=mpif90'                                                                                                      |
|  'CPPFLAGS=   '                                                                                                   |
|  'LIBS=   '                                                                                                       |
 -------------------------------------------------------------------------------------------------------------------
 -----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=2.23225, Active time=2.14445                                                    |
 -----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| DofMap                                                                                                          |
|   add_neighbors_to_send_list()     4          0.0011      0.000274    0.0011      0.000274    0.05     0.05     |
|   build_sparsity()                 4          0.0097      0.002420    0.0125      0.003133    0.45     0.58     |
|   create_dof_constraints()         4          0.0010      0.000255    0.0010      0.000255    0.05     0.05     |
|   distribute_dofs()                4          0.0015      0.000371    0.0107      0.002665    0.07     0.50     |
|   dof_indices()                    134448     0.0322      0.000000    0.0322      0.000000    1.50     1.50     |
|   old_dof_indices()                24192      0.0070      0.000000    0.0070      0.000000    0.33     0.33     |
|   prepare_send_list()              5          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         4          0.0092      0.002293    0.0092      0.002293    0.43     0.43     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_solution_vector()          8          0.0069      0.000868    0.0094      0.001172    0.32     0.44     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        96720      0.1698      0.000002    0.1698      0.000002    7.92     7.92     |
|   init_shape_functions()           43732      0.3629      0.000008    0.3629      0.000008    16.92    16.92    |
|   inverse_map()                    82656      0.0580      0.000001    0.0580      0.000001    2.71     2.71     |
|                                                                                                                 |
| FEMSystem                                                                                                       |
|   assemble_qoi()                   20         0.0278      0.001390    0.1281      0.006407    1.30     5.98     |
|   assemble_qoi_derivative()        4          0.0082      0.002055    0.0288      0.007193    0.38     1.34     |
|   assembly()                       4          0.0216      0.005406    0.0411      0.010267    1.01     1.92     |
|   assembly(get_jacobian)           4          0.0233      0.005827    0.0434      0.010850    1.09     2.02     |
|   assembly(get_residual)           20         0.0436      0.002182    0.1352      0.006759    2.04     6.30     |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_affine_map()             96720      0.0879      0.000001    0.0879      0.000001    4.10     4.10     |
|   compute_face_map()               3360       0.0049      0.000001    0.0127      0.000004    0.23     0.59     |
|   init_face_shape_functions()      28         0.0000      0.000002    0.0000      0.000002    0.00     0.00     |
|   init_reference_to_physical_map() 43732      0.1531      0.000004    0.1531      0.000004    7.14     7.14     |
|                                                                                                                 |
| GMVIO                                                                                                           |
|   write_nodal_data()               8          0.0935      0.011692    0.0935      0.011692    4.36     4.36     |
|                                                                                                                 |
| GenericProjector                                                                                                |
|   operator()                       6          0.0159      0.002648    1.3864      0.231067    0.74     64.65    |
|   project_edges                    8064       0.0005      0.000000    0.0005      0.000000    0.02     0.02     |
|   project_interior                 8064       0.0009      0.000000    0.0009      0.000000    0.04     0.04     |
|   project_nodes                    8064       0.0237      0.000003    1.3610      0.000169    1.10     63.46    |
|   project_sides                    8064       0.0005      0.000000    0.0005      0.000000    0.02     0.02     |
|                                                                                                                 |
| ImplicitSystem                                                                                                  |
|   adjoint_solve()                  4          0.0001      0.000013    0.1671      0.041764    0.00     7.79     |
|                                                                                                                 |
| Mesh                                                                                                            |
|   all_second_order()               1          0.0000      0.000022    0.0000      0.000022    0.00     0.00     |
|   contract()                       3          0.0011      0.000379    0.0047      0.001571    0.05     0.22     |
|   find_neighbors()                 6          0.0116      0.001931    0.0116      0.001931    0.54     0.54     |
|   renumber_nodes_and_elem()        3          0.0036      0.001192    0.0036      0.001192    0.17     0.17     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         8          0.0001      0.000009    0.1030      0.012873    0.00     4.80     |
|                                                                                                                 |
| MeshRefinement                                                                                                  |
|   _coarsen_elements()              3          0.0001      0.000024    0.0001      0.000024    0.00     0.00     |
|   _refine_elements()               8          0.0134      0.001680    0.0270      0.003369    0.63     1.26     |
|   add_node()                       36828      0.0102      0.000000    0.0102      0.000000    0.48     0.48     |
|   make_coarsening_compatible()     3          0.0018      0.000598    0.0018      0.000598    0.08     0.08     |
|   make_flags_parallel_consistent() 6          0.0006      0.000101    0.0006      0.000101    0.03     0.03     |
|   make_refinement_compatible()     3          0.0001      0.000028    0.0001      0.000028    0.00     0.00     |
|                                                                                                                 |
| NewtonSolver                                                                                                    |
|   solve()                          4          0.0006      0.000141    0.2189      0.054728    0.03     10.21    |
|                                                                                                                 |
| OldSolutionValue                                                                                                |
|   Number eval_at_node()            72576      0.0049      0.000000    0.0049      0.000000    0.23     0.23     |
|   check_old_context(c,p)           40320      0.0222      0.000001    0.0542      0.000001    1.04     2.53     |
|   eval_at_point()                  40320      0.6435      0.000016    1.3235      0.000033    30.01    61.72    |
|                                                                                                                 |
| Parallel                                                                                                        |
|   allgather()                      4          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   single_partition()               6          0.0004      0.000064    0.0004      0.000064    0.02     0.02     |
|                                                                                                                 |
| PetscLinearSolver                                                                                               |
|   solve()                          8          0.2427      0.030336    0.2427      0.030336    11.32    11.32    |
|                                                                                                                 |
| System                                                                                                          |
|   project_vector(old,new)          6          0.0066      0.001093    1.3958      0.232635    0.31     65.09    |
|                                                                                                                 |
| TopologyMap                                                                                                     |
|   init()                           8          0.0162      0.002023    0.0162      0.002023    0.75     0.75     |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            748071     2.1445                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------

 
***************************************************************
* Done Running Example adjoints_ex2:
*   example-opt  
***************************************************************
</pre>
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